\begin{figure}[htb]
    \centering
        \includegraphics[width=0.85\linewidth]{images//sound.jpg}
        \caption{A snapshot of our 2D sound propagation model.}
    \label{}
\end{figure}

%\subsection{Our Representation of Sound Packet}

An ideal sound propagation method should meet the following requirements.

\begin{itemize}
  \item Efficiency. One of the primary concerns in acoustics simulation, especially interactive application such as computer game and virtual reality, is the computational and memory requirements \cite{Mehra201283}. The algorithm should be real-time or real-time in the condition of using pre-computation which is often achieved through offline pre-computation of impulse responses and real-time convolution of the impulse responses.
      %In this sense, only raytracing and cellular automata are suitable.
  \item Completeness. We want to describe the sound wave's behavior completely, especially the phenomena that will influence pedestrian's localization and behavior, including reflection, attenuation, and diffraction. The physical values that real human are sensitive to should be included, other values (e.g. phase) might be ignored to save memory and time. (Although for certain wavelength, phase can contribute to human auditory perception \cite{springerlink:10.3758/BF03211932}, compared to the high cost of solving PDE, we choose to ignore phase.)
  \item Compatibility with localization. Cellular automata is suitable to be integrated with sound localization, which will be described in the next section.
\end{itemize}

%The ?rst frequency band was generated by a force normal to the surface, is well known in the literature, and was concentrated in the low-frequency range below 500 Hz

%The algorithm can be executed in multi-resolution, and resolution can be adjusted according to the requirement of accuracy and speed.

%In crowd simulation, walker's step contains high frequency part which can be efficiently solved by raytracing method, and low frequency part suitable for numerical approaches.
Experiment shows that the low frequency part of human walker's step concentrates below 500 Hz \cite{ekimov:762}, which will generate significant diffraction and scatter effect. In this paper, our simulation is limited to low frequency band whose effect is most noticeable, and thus we choose the transmission line matrix (TLM) method as discussed in the related work.
%, a cellular automata based method which is the most efficient among above methods except raytracing method, which has some problem simulating low frequency phenomena such as diffraction \cite{UKV}.
%And this method also has the advantage that the resolution (length of grid) can be adjusted to satisfy different requirements: a high resolution will give an accurate result, but a reasonable medium resolution is able to demonstrate an accuracy similar to that of human's audition.

%TODO: In this section, we want to describe that there are many concerns in virtual acoustics. For example, in an immersive system, the synthesis and rendering are the most important parts. In our system, we will adapt the acoustics model which 1) allows us to model sound's propagation as well as other effects such as reflection, attenuation, etc. that will impact the sound signal transmission within the scene, and 2) suitable for agent's localization model which will be described in the following sections. For example, ray based and cell automata based acoustics models must have different localization schemes, so we need to justify why we choose the latter one.
